This paper explores the use of stacked intelligent metasurfaces (SIM) to enhance the performance of multi-user multiple-input single-output (MISO) wireless systems. SIM, an advanced signal processing paradigm, enables over-the-air processing of electromagnetic waves at the speed of light and offers increased computational capability compared to conventional single-layer reconfigurable intelligent surfaces. The authors propose a deep reinforcement learning (DRL) approach to jointly optimize the phase shifts of SIM meta-atoms and the transmit power allocation strategy, which is efficiently solved through continuous observation of the SIM-parametrized smart wireless environment. The proposed method outperforms conventional precoding schemes, particularly under low transmit power conditions, and demonstrates a significant improvement in sum-rate performance. Additionally, a whitening process is introduced to enhance the robustness of the DRL algorithm. Simulation results validate the effectiveness of the proposed method, showing a 2 bps/Hz sum-rate improvement over a state-of-the-art alternating optimization (AO) algorithm.This paper explores the use of stacked intelligent metasurfaces (SIM) to enhance the performance of multi-user multiple-input single-output (MISO) wireless systems. SIM, an advanced signal processing paradigm, enables over-the-air processing of electromagnetic waves at the speed of light and offers increased computational capability compared to conventional single-layer reconfigurable intelligent surfaces. The authors propose a deep reinforcement learning (DRL) approach to jointly optimize the phase shifts of SIM meta-atoms and the transmit power allocation strategy, which is efficiently solved through continuous observation of the SIM-parametrized smart wireless environment. The proposed method outperforms conventional precoding schemes, particularly under low transmit power conditions, and demonstrates a significant improvement in sum-rate performance. Additionally, a whitening process is introduced to enhance the robustness of the DRL algorithm. Simulation results validate the effectiveness of the proposed method, showing a 2 bps/Hz sum-rate improvement over a state-of-the-art alternating optimization (AO) algorithm.